Understanding the complex multicellular organisms has long focused on gene networks (because genes interact) but of equal importance is the dynamics of cell populations (because cells interact). A tissue is a cell society comprised of a variety of cell types whose the relative numbers are held at a stable, defined ratio despite the fact that these cells grow (divide) at distinct rates. How does the tissue ensure stability of cell type identities and tissue composition yet allows for flexibility, e.g. during regeneration when cell types and their ratios change? From single-cell resolution analysis we now know that any cell population, even of a single type, is actually a heterogeneous mix of subpopulations of different (sub)types. Therefore, cell population dynamics is more complex than originally thought. Traditional models must be revised to integrate all the following properties in one formalism: 1.Non-genetic heterogeneity, the co-existence of cells in distinct (meta)stable states x_i (functional states, subtypes) forming subpopulations i of size n_i which collectively define a stable population state n; 2. State transitions between these subpopulations, i to j, possibly reversible, at rates M_ij; 3. Net growth rates g_i that differ in these subpopulations, allowing for competition; and 4. Cell-cell interactions via specific signals (within and between subpopulations) that may affect M_ij or g_i. None of existing theories of the dynamics of an ensemble of entities, ranging from ecologies to chemical reactions to cell populations, consider all these elements. Hence, a new theoretical framework, nonlinear population balance analysis which is based on the broader theory of non-linear stochastic dynamical system is proposed. The scholarly goal of this collaborative project is to advance THEORY but it involves EXPERIMENTS that use a combination of single-cell (sc) RNASeq and a newly invented cell-barcode method to overcome the shortcoming of scRNASeq which allows only destructive snapshot measurements. PART I (THEORY) will first establish a formal framework to describe the relationship of growth and transition rates under cell-cell interactions and the abundance n_i of subpopulations to predict existence of (multiple) stable population configurations n (Aim 1). A modeling framework to analyze the barcode data will be developed (Aim 2). PART II (EXPERIMENT) will measure these quantities with scRNASeq to determine the transcriptomes that define the cell state xi in 1000s of cells and identify the subpopulations. This will be combined with a new method of cell-unique, inherited and expressed DNA-barcodes that will permit the tracking cell lineage dynamics that reveals dynamics about growth and state transition rates (Aim 3). Applying this analysis to mixed cultures of cancer cells and fibroblasts (with implications for cancer) whose interactions will be manipulated by neutralizing antibodies (Aim 4), the theory predictions, whose chief novelty is the role of interactions, will be tested. This project is not ad hoc ?mathematical modeling? of a given instance, which is common in systems biology, but develops a general theory of a class of systems which plays an eminent role for metazoan biology and in doing so will facilitate future efforts in modelling of a variety of specific instances.